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We consider one of the quantum key distribution protocols recently introduced in Ref. [Pirandola et al., Nature Phys. 4, 726 (2008)]. This protocol consists of a two-way quantum communication between Alice and Bob, where Alice encodes secret information via a random phase-space displacement of a coherent state. In particular, we study its security against a specific class of individual attacks which are based on combinations of Gaussian quantum cloning machines.